Christopher is 4 times as old as Luis. Eight years ago, Christopher was 6 times as old as Luis. How old is Luis now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Luis. Let Christopher's current age be $c$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $c = 4l$ Eight years ago, Christopher was $c - 8$ years old, and Luis was $l - 8$ years old. The information in the second sentence can be expressed in the following equation: $c - 8 = 6(l - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = 4l$ . Substituting this into our second equation, we get: $4l$ $-$ $8 = 6(l - 8)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $4 l - 8 = 6 l - 48$ Solving for $l$ , we get: $2 l = 40.$ $l = 20$.